Answer
$k= 0$
Work Step by Step
Given $$\begin{aligned}
f(x) &= a(x-h)^2+ k.
\end{aligned}$$ The vertex $(h,k)$ of a parabola will be on the horizontal axis if its $y$-coordinate is $0$. Hence the vertex will be on the horizontal axis if $k= 0$ regardless of the values of $a$ and $h$.
